-2x^2-3/2x=0 eching

$$-2 { x }^{ 2 } - \frac{ 3 }{ 2 } x=0$$

x uchun yechish

$$x=-\frac{3}{4}=-0,75$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(-2x-\frac{3}{2}\right)=0$$

Tenglamani yechish uchun x=0 va -2x-\frac{3}{2}=0 ni yeching.

$$x=0 x=-\frac{3}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-2x^{2}-\frac{3}{2}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, -\frac{3}{2} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{3}{2}\right)±\sqrt{\left(-\frac{3}{2}\right)^{2}}}{2\left(-2\right)}$$

\left(-\frac{3}{2}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{3}{2}\right)±\frac{3}{2}}{2\left(-2\right)}$$

-\frac{3}{2} ning teskarisi \frac{3}{2} ga teng.

$$x=\frac{\frac{3}{2}±\frac{3}{2}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{\frac{3}{2}±\frac{3}{2}}{-4}$$

x=\frac{\frac{3}{2}±\frac{3}{2}}{-4} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{3}{2} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{3}{-4}$$

3 ni -4 ga bo'lish.

$$x=-\frac{3}{4}$$

x=\frac{\frac{3}{2}±\frac{3}{2}}{-4} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{3}{2} ni \frac{3}{2} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{3}{4} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-2x^{2}-\frac{3}{2}x=0$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-\frac{3}{2}x}{-2}=\frac{0}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{\frac{3}{2}}{-2}\right)x=\frac{0}{-2}$$

-\frac{3}{2} ni -2 ga bo'lish.

$$x^{2}+\frac{3}{4}x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x^{2}+\frac{3}{4}x=0$$

\frac{3}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{8} olish uchun. Keyin, \frac{3}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{4}x+\left(\frac{3}{8}\right)^{2}=\left(\frac{3}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{8} kvadratini chiqarish.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=\frac{9}{64}$$

x^{2}+\frac{3}{4}x+\frac{9}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{8}\right)^{2}=\frac{9}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{8}\right)^{2}}=\sqrt{\frac{9}{64}}$$

Qisqartirish.

$$x+\frac{3}{8}=\frac{3}{8} x+\frac{3}{8}=-\frac{3}{8}$$

Tenglamaning ikkala tarafidan \frac{3}{8} ni ayirish.

$$x=0 x=-\frac{3}{4}$$